How to quickly equalize pressure in a low pressure container?

I'm assuming you mean the air pump is connected to the sealed bucket seperately from the tube you use to suck water into the bucket? if so, maybe just glueing a rubber disc infront of the tube sucking the water (bucket end) should do the trick. When there's vacuum inside the bucket, water shouldn't have any trouble pushing the rubber flap open, but when pressure equalises, the rubber would seat back over the tube, stopping the water flow. Can't say i've tried anything like this, just a theory.

edit- again with the rubber flaps idea, if you drill a hole in the top of the bucket and glue another flap on the top of it, when you turn the pump off just lift the flap and that'll equalise pressure double quick!

You don't show a diagram of the setup, but change the pipe entry point to the tank - put it at the bottom then you should prevent the syphon effect. The depression you create with the pump will still cause the water to get into the tank and, while the depression holds the water will stay in the tank as long as it is sealed...

Just add a valve (manual or solenoid valve) at water suction line. When you want to stop syphoning, just close the valve.

Figure 1. The solution is to ensure that the pail fill pipe is above the maximum liquid level.